The Blaugrana began the game at the Rosaleda without either forward in their starting line-up, with Messi having been ruled out of the game with a thigh injury and coach Gerardo Martino continuing to carefully manage second-half substitute Neymar, who lost seven kilograms after having his tonsils removed during pre-season.
That Barcelona still managed to take home all three points thanks to a goal from Adriano is testament to the Catalans' strength in depth, according to Fabregas.
“The team does not depend on Messi and Neymar," the attacking midfielder is quoted as saying by his club's official website. "We’re all important. We all have responsibilities in the team.
“We really had a hard time in the final minutes of the match, but we have to be able to get through the hard times.
"We’re starting a new season, with lots of new things, we have to keep on improving.
“We had a good first half, but it’s true that in the second we lost a bit of intensity.
"We’re still feeling the Super Cup match [against Atletico Madrid in midweek], and it was noticeable, so this was a very, very important victory.
“We could have scored more goals, we had the chances to do so, but we didn’t score and we suffered in the final minutes."
Fabregas has been repeatedly linked with a move to Manchester United this summer but he remains as focused as ever on nailing down a regular berth in the Catalan side's starting XI.
“I always try to do a good job," the former Arsenal captain explained. "I want to continue improving. The fans want more from me and I have to give it.
"I know what the manager wants from me, starting from there, I try to work to win the manager’s confidence."
Barca host Atletico Madrid in the second leg of the Spanish Super Cup on Wednesday, after drawing the first leg 1-1 at Vicente Calderon.
